The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index; none of the 8 sources its claims cite is checked for support yet.
A fast quantum mechanical algorithm for database search
Open accessAbstract
An unsorted database contains N records, of which just one satisfies a particular property.The problem is to identify that one record.Any classical algorithm, deterministic or probabilistic, will clearly take O (N) steps since on the average it will have to examine a large fraction of the N records.Quantum mechanical systems can do several operations simultaneously due to their wave like properties.This paper gives an O ( JN) step quantum mechanical algorithm for identifying that record.It is within a constant factor of the fastest possible quantum mechanical algorithm.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
19 No basis given · 8 Sources not found · 4 Own interpretation
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This paper gives an O ( JN) step quantum mechanical algorithm for identifying that record.”
§ A fast quantum mechanical algorithm for database search > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Corollary 3.1-Let the state vector be as followsfor any one state the amplitude is k, for each of the remaining (N-1) states the amplitude is 1.Let k and 1 be real numbers (in general the amplitudes can be complex).Let k be negative and 1 be positive such that ~< ~N.Then after applying the diffusion transform both k and 1are positive numbers.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“First, it is proved that the system is a valid quantum mechanical system (theorems 1 & 2)”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As mentioned in the introduction, the algorithm of this paper does not use any Imowledge about the problem.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Theorem 1-The matix D is unitary.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The following sections prove that the system discussed in section 3 is indeed a valid quantum mechanical system and that it converges to the desired state with a probability O(l).”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Theorem 2 -D can be expressed as D = FRF, where F, the Fourier Transform Matrix and R, the rotation matrix are defined as follows”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since the proba-& bility of the system being found in any particular state is proportional to the square of the amplitude, it follows that the probability of the system being in tlhe desired state when k is ~, 1 J2 is k2 = ~.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In case there is a unique state SV such that C(SV) = 1, the final state is SV with a probability of at least ~. 2”
§ A fast quantum mechanical algorithm for database search > T. Acknowledgments
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
- The authors state this as an assumption: There is a unique state that satisfies the condition C(S)=1.
- The authors state this as an assumption: For any state S, the condition C(S) can be evaluated in unit time.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It can be easily modified to take care of the case when there are multiple states satisfying the condition C(S) = 1 and it is required to return one of these.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Probably not a substantial claim. 8
- It may state two separate claims as one. 4
- The quote only partly states this claim. 1
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Theorem 5-Let the probability of a particular outcome in an experiment be &.Then if the experiment be repeated ~times, the probability that the outcome does not happen even once is less than or equal to e-K.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The change in k ( Ak) after steps (a) and (b) of the algorithm is lower bounded by Ak>~.Also after steps (a) and (b), 1>0.2fi”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using this it immediately follows that there exists a number M less than EN, such that in M repetitions of the loop in step (ii), k wifl become ~.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The most efficient classical algorithm for this is to examine the items in the database one by one.”
§ A fast quantum mechanical algorithm for database search > ------------------------------------------------
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Very recent results [Shor95] have shown the existence of quantum mechanical error corr~ting cod~which enable transmission of data even in the presence of noise”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [Shor95]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This algorithm, by cleverly making use of some features of the structure of the problem, is the only known algorithm that solves the problem in O (logIV) steps.”
§ A fast quantum mechanical algorithm for database search > 114
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The phase does not have an analog in classical probabilistic algorithms.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This illustrates the point that, in quantum mechanics, the complete description of the system requires the amplitudes over all states, just the probabilities is not enough.”
§ A fast quantum mechanical algorithm for database search > 1.1 Search Problems in Computer Science
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“For example Shor's primality testing algorithm [Shor94] for a number N can be viewed as a search of the (N-l) numbers smaller than N to see if any of them is a factor of N.”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [Shor94]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“There is also a scheme discussed in [VV86] by which it is possible to modify any algorithm that solves an NPsearch problem with a unique solution and use it to solve an NP-search problem in general.”
§ A fast quantum mechanical algorithm for database search > 114
What the sources say
- Not matchedcites [VV86]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“This operation is one of the things that makes quantum mechanical algorithms more powerful than classical algorithms and forms the basis for most significant quantum mechanical algorithms.”
§ A fast quantum mechanical algorithm for database search > T. Acknowledgments
What the sources say
- Not matchedcites [DJ92]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
The authors state this as an assumption.
There is a unique state that satisfies the condition C(S)=1.
“Let there be a unique state, say Sv, that satisfies the condition C(SV) = 1, whereas for all other states S, C(S) = 0”
“The algorithm as discussed here assumes a unique state that satisfies the desired condition.”
The authors state this as an assumption.
For any state S, the condition C(S) can be evaluated in unit time.
“(assume that for any state S, the condition C(S) can be evaluated in unit time)”
The paper relies on this without support.
There does not exist any sorting on the database that would aid selection of the desired item.
“However, there does not exist any sorting on the database that would aid its selection.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Symmetric cryptography remains comparatively resilient, yet Grover's algorithm offers a quadratic speed-up for brute-force key search, effectively halving the security margin of symmetric ciphers [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Similarly, for hash functions, Grover's algorithm [185] can facilitate quantum birthday attack to find collision, thereby necessitating an output of larger size.”
From Zero Trust Architecture (ZTA): A Comprehensive Survey (2022) · cites this paper as [185]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Similarly, Grover’s algorithm concedes a quadratic advantage for mining blocks in certain consensus protocols such as proof of work.”
From Quantum-resistance in blockchain networks (2023) · cites this paper as [71]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Quantum computers will be able to find these nonces quadratically faster using Grover’s algorithm71.”
From Quantum-resistance in blockchain networks (2023) · cites this paper as [71]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This model is realistic given the falling cost of storage, the rise of large-scale surveillance infrastructures, and the expected disruption of quantum algorithms such as Shor's and Grover's [1,2,13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measured
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Grover's algorithm provides only a quadratic speedup, effectively halving brute-force resistance. Comparable security margins can be restored by doubling key sizes (for example, AES-128 to AES-256) [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This explains why AES-256 maintains post-quantum security margins, whereas AES-128 requires upgrading to maintain equivalent protection levels [13,14].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“At the same time, Grover's algorithm shows that symmetric cryptography, though more resilient, also demands doubled key sizes to maintain equivalent margins [13].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In this sense, Grover-based optimization algorithms [184] such as Grover Adaptive Search [161] have been proposed.”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [184]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The former bound is tight since recent work of Grover [13] shows how to accept the class NP relative to any oracle on a quantum computer in time O (2 n/ 2 ).”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In view of Grover's algorithm [13], we know that the constant '1 / 2' in the statement of Theorem 3.5 cannot be improved.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The former bound is tight since recent work of Grover [13] shows how to accept the class NP relative to any oracle on a quantum computer in time O (2 n/ 2 ).”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Grover’s algorithm [54] is a quantum algorithm for searching in a database, ofering quadratic speedup over classical searching methods.”
From QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation (2023) · cites this paper as [54]
The cited source says what the claim attributes to it.
In the citing paper
“However, quantum machines can recognize this language quadratically faster, in time O ( √ 2 n ), using Grover's algorithm [13].”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The cited source says what the claim attributes to it.
In the citing paper
“That this was a real possibility is clear from Grover's [13] result, which gives a black-box approach to solving NP -complete problems in square-root as much time as is required classically.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The cited source says what the claim attributes to it.
In the citing paper
“Various strategies can be imagined, but a good one (called 'inversion about the average' by Grover [13]) is to perform an oracle-independent unitary transformation so as to change the phase difference into an amplitude difference, leaving the y term with the same sign as all the other terms but a magnitude approximately threefold larger.”
From Strengths and Weaknesses of Quantum Computing (1997) · cites this paper as [13]
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“The HNDL adversary departs from conventional cryptanalysis in its temporal asymmetry. Instead of attempting immediate decryption, the attacker passively collects encrypted traffic or stored archives and defers decryption until sufficient computational resources become available.”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [13]
Experimental — accuracy not yet measuredIn the citing paper
“This algorithm uses a single function evaluation to label the single state which satisfies the function, followed by a series of gates which drive the system into this particular state.”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“Here we show how such a computer can be used to implement a fast quantum search algorithm initially developed by Grover. 9, 10”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“Among other applications Grover's algorithms enable an extremely rapid search over the domain of a binary function to find elements for which this function is satisfied (that is, the function has the value 1).”
From Implementation of a quantum search algorithm on a quantum computer (1998) · cites this paper as [9]
In the citing paper
“the ability to efficiently perform Hamiltonian simulation is used in conjunction with another technique known as the quantum phase estimation algorithm (QPEA) 42 for efficiently obtaining the eigen-energies and eigenstates of a quantum system 38 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“The Quantum Phase Estimation (QPE) algorithm 38,99 is the natural translation of the FCI procedure to quantum computers 45 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“Abrams and Lloyd 38 focused on state preparation in more detail and described concrete initialization procedures.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
In the citing paper
“They pointed out that state preparation is conceptually easier in second quantization, where a Fock state is represented by a simple product state of qubits in {| 0 〉 , | 1 〉} states.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [38]
Citations
Cites
Algorithms for quantum computation: discrete logarithms and factoring
Shor, P. W. (2002) · Proceedings 35th Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.1994.365700 · Cited by 8,713
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Rapid solution of problems by quantum computation
Deutsch, D., & Jozsa, R. (1992) · Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences · doi:10.1098/rspa.1992.0167 · Cited by 2,700
The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics
Penrose, R., & Gardner, M. (1989) · doi:10.1093/oso/9780198519737.001.0001 · Cited by 2,007
Strengths and Weaknesses of Quantum Computing
Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796300933 · Cited by 1,470
On the Power of Quantum Computation
Simon, D. R. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539796298637 · Cited by 1,295
Bernstein, E., & Vazirani, U. (1993) · Proceedings of the twenty-fifth annual ACM symposium on Theory of computing - STOC '93 · doi:10.1145/167088.167097 · Cited by 1,284
Benioff, P. (1980) · Journal of Statistical Physics · doi:10.1007/bf01011339 · Cited by 1,244
The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
Penrose, R., & Landauer, R. (1990) · Physics Today · doi:10.1063/1.2810599 · Cited by 1,110
Research works printed but not linked: 2
- [9]9. R. Penrose, Shadows of the mind,. Oxford University Press, 1994, pp. 348- 388.
- [14]14. Yao93J A. Yao, Quantum circuit complexip, Proceedings 34th Annual Symposium on Foundations of Computer Science (FOCS), 1993, pp. 352-361.
Cited by
Sorted by citations
Items 6,701–6,800 of 8,792
Comparizon of dynamic diffusion with explicit difference scheme for Shredinger equationPreprint
Kukushkin, V., & Ozhigov, Y. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1105.0518
Algebra geometrica e o algoritmo de Grover
Alves, R. S. D. O. (2008) · doi:10.47749/t/unicamp.2008.426392
Quantum Computation Perspectives in Medical Image Processing
Rodrigues, P., Ferreira, M. J., & Monteiro, J. L. (2010) · International Journal of Nanotechnology and Molecular Computation · doi:10.4018/978-1-61520-670-4.ch006
A Time-Efficient Output-Sensitive Quantum Algorithm for Boolean Matrix Multiplication
Gall, F. L. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35261-4_66
Multi-party Quantum Communication Complexity with Routed Messages
Tani, S., Nakanishi, M., & Yamashita, S. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-69733-6_19
Quantum Algorithm for Finding Triangles
Jeffery, S., & Richter, P. C. (2016) · Springer eBooks · doi:10.1007/978-1-4939-2864-4_308
Simulations of error in quantum adiabatic computations of random 2-SAT instances
Gill, J. S. (2006) · DSpace@MIT (Massachusetts Institute of Technology)
Optimisation of Quantum Hamiltonian Evolution: Two Projection OperatorsPreprint
Patel, A. D., & Priyadarsini, A. (2015) · arXiv (Cornell University)
Entanglement in systems of oscillators and quantum computationsPreprint
Ozhigov, Y. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1209.0747 · Cited by 1
The Computational Power of Non-interacting Particles
Brod, D. J. (2014) · Americanae (AECID Library) · doi:10.48550/arxiv.1412.7637
Monte Carlo simulations in open quantum systems.
Ryn, N. V. (2007) · ResearchSpace (University of KwaZulu-Natal)
Incremental information extraction from Grover's algorithm
Jacobs, B. C., Pittman, T. B., & Franson, J. D. (2004) · doi:10.5555/984720.984760
Quantum Sampling for Balanced Allocations
Iwama, K., Kawachi, A., & Yamashita, S. (2003) · Lecture notes in computer science · doi:10.1007/3-540-45071-8_32
Studies in quantum information theory
Menicucci, N. C. (2008)
Hadamard’s Matrices, Grothendieck’s Constant, and Root Two
Fortin, D. (2010) · Springer optimization and its applications · doi:10.1007/978-0-387-89496-6_20
Investigating Photonic Quantum Computation
Myers, C. R. (2007) · UWSpace (University of Waterloo)
Bassa, H. (2013) · ResearchSpace (University of KwaZulu-Natal)
QoS Route Discovery of Ad Hoc Networks Based on Intelligence Computing
Jin, C., & Jin, S. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-87732-5_92
Search via quantum walks with intermediate measurements
Buksman, E., de Oliveira, A. L. F., & de Lacalle, J. G. L. (2015) · International Journal of Modern Physics B · doi:10.1142/s0217979215501271
Hiding Quantum States in a SuperpositionPreprint
Younes, A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0807.4732
Solving Hard Problems on Adiabatic Quantum Computers
Ciocirlan, D., Ţăpuş, N., & Dragomir, D. (2015) · International Conference on Control Systems and Computer Science · doi:10.1109/cscs.2015.100
Quantum Information: an invitation for mathematicians
Pérez-Garcı́a, D., Etayo, F., Fioravanti, M., & Santamaría, R. (2009) · AIP conference proceedings · doi:10.1063/1.3146236
Dynamic Portfolio Selection to Counter Terrorism by using Quantum Neural Network Approach
Ahmad, F. (2015) · Computer Engineering and Intelligent Systems
Analysis of the Entanglement Cost and Calculation of the Holevo CapacityPreprint
Shimono, T. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0610178
An Algorithm to Speed Up Quantum SearchPreprint
Martinelli, G., & Panella, M. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0609176
Entanglement in Valence-Bond-Solid States and Quantum Search
Xu, Y. D. (2009) · SUNY Digital Repository Support (State University of New York System)
Exploiting Particle Statistics in Quantum ComputationPreprint
Castagnoli, G., & Monti, D. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9806086
Quantum Harmonic Sieve: Learning DNF with a Classical Example OraclePreprint
Ventura, D. A., & Martinez, T. R. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9805043
Generation of topologically useful entangled statesPreprint
Lovett, N. B., & Varcoe, B. T. H. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1101.1220 · Cited by 1
Quantum optical device accelerating dynamic programmingPreprint
Grigoriev, D. Y., Kazakov, A. Y., & Vakulenko, S. A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0506081
Breaking Classical Public Key Cryptosystems by Using a Novel Ensemble Search AlgorithmPreprint
Chen, C.-Y. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0407126
Semantic Network LayeringPreprint
Neufeld, M., & Partridge, C. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0902.4221
A POSSIBLE APPLICATION OF QUANTUM ALGORITHM FOR MARKET PRICE PREDICTION
Nayak, S., Nayak, S., & Singh, J. (2013) · Journal of Global Research in Computer Sciences
Decoherence in semiconductor solid-state quantum computers
Valente, D. C. B. (2009) · Journal of International Crisis and Risk Communication Research
Single Photon Near Field Emission and Revival in Quantum DotsPreprint
Tafur, S., & Leuenberger, M. N. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1011.6566
The limits of predictability : indeterminism and undecidability in classical and quantum physics
Korolev, A. (2011) · cIRcle (University of British Columbia) · doi:10.14288/1.0302406
A note on quantum one-way permutationsPreprint
Kashefi, E., Nishimura, H., & Vedral, V. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0109157 · Cited by 1
Note on Needle in a HaystackPreprint
Burger, J. R. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.cs/0308043
On the Complexity of Quantum Searching Using Complex QueriesPreprint
Grassl, M., & Beth, T. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9706052
Quantum Sorting and Route Finding
Wallace, J. (2002) · AIP conference proceedings · doi:10.1063/1.1503697
Novel Identification of Symmetric and Anti-Symmetric Quantum FunctionsPreprint
Burger, J. R. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0308157
Ensemble Algorithm for the Selection Problem by NMR Ensemble Quantum ComputersPreprint
Chen, C.-Y., & Hsueh, C.-C. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0407109
Roland, J., & Cerf, N. J. (2004) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · Cited by 1
Finding quantum algorithms via convex optimization
Childs, A. M., Landahl, A. J., & Parrilo, P. A. (2007) · European Control Conference (ECC) · doi:10.23919/ecc.2007.7069011
Analog quantum neuron for functions approximation
Ezhov, A. A., Khromov, A. G., & Berman, G. P. (2002) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2001.939600
Implications of the Luders Postulate for Quantum AlgorithmsPreprint
Meister, B. K. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0509052
A reduction from LWE problem to dihedral coset problemPreprint
Li, F., Bao, W., Fu, X.-Q., Zhang, Y., & Li, T. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1305.3769
Non-classical Aspects in Proof Complexity
Beyersdorff, O. (2012) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York)
Nguyen, H. T., Крейнович, В., Gamez, J. E., et al. (2009) · Studies in computational intelligence · doi:10.1007/978-3-642-01533-5_3
Introduction to Quantum Information/Computing
Costianes, P. J. (2005) · doi:10.21236/ada436335
Codigos convolucionais quanticos concatenados
de Almeida, A. C. A. (2004) · doi:10.47749/t/unicamp.2004.322954
Performance Evaluation of Three Kinds of Quantum Optimization
Chang, B. R., & Tsai, H. F. (2007) · Springer eBooks · doi:10.1007/978-3-540-74581-5_24
Relativistic Quantum Communication
Hosler, D. (2013) · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · doi:10.48550/arxiv.1306.4853
Rönnholm, A. (2012) · Lund University Publications Student Papers (Lund University)
Nuevos algoritmos cuánticos para tomografía de procesos y estados
Bendersky, A. (2011) · Repositorio Digital Institucional de la Universidad de Buenos Aires (Universidad de Buenos Aires)
Decoherence And Defects In Cooper-Pair Boxes
Zaretskey, V. (2013) · University Libraries (University of Maryland)
A Programming Language Oriented Approach to ComputabilityPreprint
Karper, A. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.2949
Discrete-time quantum walk with two-step memory
Jones, C. (2012)
Recovering Strings in Oracles: Quantum and Classic
Iwama, K. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-31653-1_3
Deriving the Qubit from Entropy PrinciplesPreprint
Brandenburger, A. M., & Mura, P. L. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.3365
Simulation of quantum interference by reactions of chemical typePreprint
Ozhigov, Y. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0310188
Constant-time solution to Simon's decision problem with the known subgroup range in quantum computer
Chen, C.-Y., & Hsueh, C.-C. (2007) · Computational intelligence
A Fast Natural Algorithm for Searching: Preliminary version
Arulanandham, J. J., Calude, C. S., & Dinneen, M. J. (2003)
Tarrataca, L. D. T. J., & Wichert, A. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-24971-6_17
Generator of an abstract quantum walkPreprint
Segawa, E., & Suzuki, A. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1508.07473
A C*-Algebraic Approach to Quantum Coding Theory
Steiner, L. (2008) · Technischen Universität Darmstadt · doi:10.26083/tuprints-00001000
Quantum Random Walks on the integer lattice via generating functions
Bressler, A. (2009)
TDM-based Interferometric Technique for Maintain-reduced WDM Quantum Key Distribution Network
Zhan, L., He, L., Sun, Y., et al. (2014) · Asia Communications and Photonics Conference · doi:10.1364/acpc.2014.af1h.5
Mogos, G. (2014) · International Conference on Computational Science and Computational Intelligence (CSCI) · doi:10.1109/csci.2014.130
Ntalaperas, D., & Konofaos, N. (2008) · Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics · doi:10.1002/pssc.200780184
Performance evaluation of adiabatic quantum computation using neuron-like interconnections
Sato, S., Ono, A., Kinjo, M., & Nakajima, K. (2011) · Nonlinear Theory and Its Applications IEICE · doi:10.1587/nolta.2.198
Chang, B. R., & Tsai, H. F. (2010) · Applied Soft Computing · doi:10.1016/j.asoc.2010.02.001
Chang, W.-L., Ren, T.-T., Feng, M., et al. (2010) · International Conference on Computational Aspects of Social Networks (CASoN) · doi:10.1109/cason.2010.165
Al‐Rabadi, A. N. (2012) · Intelligent Automation & Soft Computing · doi:10.1080/10798587.2012.10643229
Topological Characterizations of Automata Theory Based on Quantum Logic
Guo, X. (2007) · Journal of Software · doi:10.1360/jos181282
Non-Pauli observables for CWS codes
Santiago, D. F. G., Portugal, R., & Melo, N. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0501-9
Joint remote state preparation of a qubit state via a W state using single-atom rotation operations
Xiao, X.-Q., Lin, X., & Li, Y. (2014) · doi:10.1109/icsai.2014.7009363
The amplified quantum Fourier transform: solving the local period problem
Cornwell, D. J. (2012) · Quantum Information Processing · doi:10.1007/s11128-012-0468-6
Complexity of solving nonlinear equations in the deterministic, randomized and quantum settings
Goćwin, M., & Kacewicz, B. Z. (2013) · Applied Mathematics and Computation · doi:10.1016/j.amc.2013.09.008
Applied Technology in Multidimensional Color Image Scaling Based on NASS in a Quantum System
Li, H. S., & Song, K. (2014) · Advanced materials research · doi:10.4028/www.scientific.net/amr.1046.411
Lower Bounds on Quantum Query Complexity for Read-Once Formulas with XOR and MUX Operators
Fukuhara, H., & Takimoto, E. (2010) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.e93.d.280
Iwama, K., Kawachi, A., & Yamashita, S. (2005) · IPSJ Digital Courier · doi:10.2197/ipsjdc.1.461
Quantenphysik und die Zukunft der Kryptographie
Kaijser, P., & Markwitz, W. (2008) · Datenschutz und Datensicherheit - DuD · doi:10.1007/s11623-008-0095-7
ACM SIGACT News Distributed Computing Column 31
Keidar, I. (2008) · ACM SIGACT News · doi:10.1145/1412700.1412716
Cheng-dong, C., & Chang, X. (2011) · International Conference on Artificial Intelligence, Management Science and Electronic Commerce · doi:10.1109/aimsec.2011.6010077
Algebraic Problems in Computational Complexity
Sen, P. K. (2001) · University
Quantum Multi-object Search Algorithm with the Availability of Partial Information
Chen, G., & Diao, Z. (2001) · Zeitschrift für Naturforschung A · doi:10.1515/zna-2001-1215
Will quantum chemistry benefit from quantum computers?
Kaijser, P. (2009) · International Journal of Quantum Chemistry · doi:10.1002/qua.22062
Quantum recognition of eigenvalues, structure of devices, and thermodynamic properties
Ozhigov, Y. I. (2003) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.1560407
Simulation and Investigation of Quantum Search Algorithm System
Li, S., & Wen-bo, X. (2006) · Lecture notes in computer science · doi:10.1007/11881223_1
A Quantum Secret Sharing Scheme with High Efficiency Based on Bell States
Li, K., Yuanyuan, L., Kehai, H., et al. (2012) · International Symposium on Information Science and Engineering · doi:10.1109/isise.2012.100
Quantum walk search factors in the regime of weak measurement
Ghoshal, D. (2014) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2050932
Macroscopic models for quantum systems and computers
Aerts, D., Czachor, M., Dehaene, J., et al. (2007) · Journal of Physics Conference Series · doi:10.1088/1742-6596/70/1/012001
The effect of sample property on optimum search by quantum computing
Fard, H. E., Jahan, M. V., & Jalali, M. (2011) · International Conference on Computer and Knowledge Engineering · doi:10.1109/iccke.2011.6413316
Model of a hybrid processor executing C++ with additional quantum functions
Elhoushi, M., El-Kharashi, M. W., & Elrefaei, H. (2014) · Microprocessors and Microsystems · doi:10.1016/j.micpro.2014.09.002
An efficient method for improving the performance of quantum boolean circuit synthesis algorithms
Wang, S.-A., & Lu, C.-Y. (2011) · doi:10.1109/icmt.2011.6002505
A New BSQDD Approach for Synthesis of Quantum Circuit
Som, A., & Chakrabarti, A. (2011) · International Symposium on Electronic System Design · doi:10.1109/ised.2011.28
A practical framework to utilize quantum search
Yamashita, S., & Nakanishi, M. (2007) · IEEE Congress on Evolutionary Computation (CEC) · doi:10.1109/cec.2007.4425004
Metadata
- Authors
- Grover, L. K.
- Affiliations
- AT&T (United States) (US)
- Corresponding author
- Grover, Lov K.
- Venue
- Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96
- Publisher
- ACM Press
- Published
- 1996
- Pages
- 212-219
- OpenAlex
- W2084652510
- Semantic Scholar
- 298d799da82395a64a3bda38ef9d2a4646828ccb
- Cited by
- 8,830
- References
- 24
- Citations by year
- 2026: 664 · 2025: 1066 · 2024: 896 · 2023: 841 · 2022: 674 · 2021: 655 · 2020: 529 · 2019: 423 · 2018: 288 · 2017: 283 · 2016: 219 · 2015: 221 · 2014: 184 · 2013: 161 · 2012: 158
- FWCI
- 36.24
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Symposium on Theory of Computing (STOC) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum search, unsorted database search, Grover's algorithm, quantum algorithms, time complexity, quantum parallelism, lower bounds
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-21, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-21 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
